Jeff McFadden, NIST

Sam Coriell, NIST

Bill Mitchell, NIST

Bruce Murray, SUNY Binghamton

Barry Andrews, U. Alabama, Birmingham

J. Arikawa, U. Alabama, Birmingham

Modeling of Flow during Coupled Monotectic Growth

NASA Physical Sciences Research Division

Lamellar Eutectic Growth Rod Monotectic Growth

Want better prediction of lamella and rod spacings (monotectics)

Al-In [Grugel & Hellawell (1981)]

[Hunt & Lu (1994)]

L1 Flow

Monotectic Flow Models

L2 S

Inter-rod Spacing

L1

z

r

Basic Domain

r

z

L1

Marangoni Flow

r

z

L2 S L2 S

U ~ VUm>> V

Circular Cap Model

Density Change

Jackson-Hunt Theory (1966)

Analytical Model:

Seetharaman and Trevedi (1988)

(But the predicted spacing is 4 to 5 times too small for some monotectics)

Density-Change Flow

Modified Jackson-Hunt Theory

Magnin & Trivedi [Acta Met. (1991)], Coriell et al. [JCG (1997)]

[Still separable, but no lateral transport…]

Inclusion of Lateral Transport

Stokes Flow (Sn-Pb)

Tangential Velocity Component (Sn-Pb)

Eutectic Lamellar Spacing (Sn-Pb)

Num

MJH

JH

(Predicted spacing consistent with experiment)

Euctectic Lamellar Spacing (Fe-C)

Num

MJH

JH

(Predicted spacing is 5 X too small)

Interface Concentration (Fe-C)

Modified Jackson-Hunt

Numerical

Monotectic Rod Spacing (Al-In)

JH

MJH

Num

(Predicted spacing is 4 X too small)

Rod Growth (Al-In)

Monotectic composition

Monotectic composition + 2.0 mass%

SummaryRelative to the Modified Jackson-Hunt theory:

•Lateral flow increases spacing for Sn-Pb, Al-In (augments diffusion)•Lateral flow decreases spacing for Fe-C (opposes diffusion)

Predicted spacings are still too small for monotectics

Current Work

Linear stability of a planar fluid-fluid phase boundary

in directional solidification (monotectic L1 – L2 transition)

Account for bouyancy, density change, Marangoni flow• Laplace-Young equation

•Gibbs-Thomson equation

•Classius-Clapyron equation